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Physical review. B, Condensed matter

Phase transitions and elementary excitations in a zigzag-like spin system

Andrei A. Zvyagin

Published Jan 1, 1998• 18 citations
Publisher

Abstract

Phase transitions in the quantum frustrated antiferromagnetic two-chain system with additional three-spin interactions of special form are studied. With the help of an exact Bethe ansatz solution it is shown that such a zigzag-like system has two critical-magnetic-field values in the ground state: One of these is the usual phase transition into a ferromagnetic state, while the second one is connected with magnetic structure doubling. Two phase transitions are revealed in the ``factorization'' of the dispersion law of an elementary excitation. The absence of a gap behavior in recent experiments is explained. Two types of chiral spin ordering for frustrated low-dimensional magnets are proposed.

DOI
10.1103/physrevb.57.1035

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Phase transitions in the quantum frustrated antiferromagnetic two-chain system with additional three-spin interactions of special form are studied. With the help of an exact Bethe ansatz solution it is shown that such a zigzag-like system has two critical-magnetic-field values in the ground state: One of these is the usual phase transition into a ferromagnetic state, while the second one is connected with magnetic structure doubling. Two phase transitions are revealed in the ``factorization'' of the dispersion law of an elementary excitation. The absence of a gap behavior in recent experiments is explained. Two types of chiral spin ordering for frustrated low-dimensional magnets are proposed.
Several exactly solvable quantum spin models with incommensurate magnetic structures, which manifest quantum phase transitions between incommensurate and commensurate phases, are proposed. The ground-state and thermodynamic characteristics of these quantum spin antiferromagnetic models with the Dzyaloshinsky-Moriya antisymmetric exchange interaction and spin-frustrating next-nearest-neighbor, three-spin, and four-spin (ring exchange) interactions are exactly studied. We investigated the ground state phases of the considered models, as function of the magnetic anisotropy, Dzyaloshinsky-Moriya interaction, next-nearest-neighbor coupling constants, and external magnetic field. Several quantum phase transitions between magnetically incommensurate phases and between incommensurate and ferromagnetic phases are predicted, and the behavior of thermodynamic characteristics of those models at phase transitions is studied. We have shown that for models with chiral three-spin interactions the Dzyaloshinsky-Moriya coupling yields the onset of the weak ferromagnetism, similar to three-dimensional ordered antiferromagnets, but not present in other quantum spin chains with the antisymmetric exchange. Considered models appeared to be important for several quasi-one-dimensional spin systems, studied in recent experiments.
The equations of the thermodynamic Bethe ansatz for two-chain and multichain quantum spin 1/2 systems are constructed. It is shown that the system is in the antichiral state for any temperature range and for any value of the external magnetic field (except for the ferromagnetic ground-state case). The elementary spin excitations carry nonzero chirality and are gapless. Those excitations are confined into pairs (singlets and triplets), with opposite sign of chiralities, so the state of the system remains antichiral at any temperature. The reason for such chiral behavior is the existence of the topological term of the Wess-Zumino nature in the Hamiltonian. We conjecture that the quantum spin (1/2) multichain system with the Hamiltonian without the topological terms has excitations with gaps.
We investigate the quantum spin-1/2 zigzag chain with frustrated ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg interactions, incorporating additional off-diagonal exchange interactions known as the $\mathrm{\ensuremath{\Gamma}}$ term, both with and without an applied magnetic field. Based on the density-matrix renormalization group calculation, we map out the ground-state phase diagram that shows a variety of magnetic and nonmagnetic phases including multicritical points and several exactly solvable points. Upon introducing a finite $\mathrm{\ensuremath{\Gamma}}$ term, we observe the persistent dimer-singlet state of the ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model, sustaining a nonzero spin gap, while also hosting a gapless nonmagnetic excitation that manifests in the substantial zero-energy peak in the nematic dynamical structure factor. This gapless peak-mode, remaining almost as a fluctuation to the ground state, induces a dilute but robust concentration of nematicity on top of singlets on dimers, which we call the nematic singlet-dimer phase. When the whole nematic excited mode condenses and replaces the singlet, the nematic-dimer phase transforms into the Ising-type ferromagnetic or antiferromagnetic long-range orders. The $\mathrm{\ensuremath{\Gamma}}$ term spontaneously selects magnetic easy axes, and their orientations dictate the type of magnetic order under geometric frustration effects as predicted by Landau's mean-field theory. These theoretical findings provide insights into the exotic low-temperature phase observed in YbCuS2{\mathrm{YbCuS}}_{2}YbCuS2​, characterized by gapless excitations and seemingly nonmagnetic behavior.
We study the zero-temperature properties of a spin-1/21/21/2 Heisenberg chain with an additional three-site chiral term of strength ggg. The model is known to be integrable and previous work using Bethe ansatz has identified a phase transition from the usual critical state for g<gc=2/πg< g_c = 2/πg<gc​=2/π to a chiral phase for g>gcg>g_cg>gc​. Here we combine analytical and computational approaches to demonstrate that the transition point comprises an unusual Lifshitz transition with dynamical critical exponent z=3z=3z=3, and the chiral phase is a partially spin-polarized phase which spontaneously breaks SU(2) symmetry. We derive a strongly interacting chiral boson field theory for the critical point, and show that even its small-momentum, low-energy response is non-trivial. We also determine the universal properties of the chiral phase, and specifically show that it has a simultaneous quadratically dispersing ferromagnetic "magnon" mode coexisting with the power-law singularities and linearly dispersing excitations typical of a Luttinger liquid. Our conclusions are validated using numerics based on matrix product state methods and exact diagonalization.
We outline the recent results on the ground state for a class of one- and two-dimensional frustrated quantum spin models with competing ferro(F)- and antiferromagnetic (AF) interactions. Frustrated spin systems are known to have many interesting properties due to large quantum fluctuations. As a result of these fluctuations usual mean-field approach gives quite crude (if not false) description of these systems. Therefore, exactly solvable models are very instructive at investigations of such systems. The exact ground state wave function of proposed models has a structure of the valence-bond state (VBS) type. One of the 1D model describes the transition line between the F and AF phase. The exact singlet ground state on this line has a double-spiral ordering. Using different approximation methods we study the magnetization curve in the AF phase. The second considered set of the 1D and 2D models has an exact non-degenerate ground state with exponentially decaying spin correlations. We also proposed the 1D and 2D electronic models with exact ground state represented in terms of singlet bond functions which are the generalization of the RVB functions including ionic states.
Quantum spin systems can break time-reversal symmetry by developing spontaneous magnetization or spin chirality. However, collinear magnets and chiral spin states are invariant under different symmetries, implying that the order parameter of one phase vanishes in the other. We show how to construct one-dimensional anisotropic spin models that exhibit a ``Landau-forbidden'' continuous phase transition between such states. As a concrete example, we focus on a zigzag chain with bond-dependent exchange and six-spin interactions. Using a combination of exact solutions, effective field theories, and numerical simulations, we show that the transition between the chiral and magnetic phases has an emergent U(1)U(1)U(1) symmetry. The excitations governing the transition from the chiral phase can be pictured as mobile defects in a Z2{\mathbb{Z}}_{2}Z2​ flux configuration which bind fermionic modes. We briefly discuss extensions to two dimensions and analogies with deconfined quantum criticality. Our results suggest new prospects for unconventional phase transitions involving chiral spin states.